We give rigidity and universality theorems for embedded deformations of Lie subgroups. If
K
⊂
H
⊂
G
K \subset H \subset G
are Lie groups, with
H
1
(
K
,
g
/
h
)
=
0
{H^1}(K,g/h) = 0
, then for every
C
∞
{C^\infty }
deformation of H, a conjugate of K lies in each nearby fiber
H
s
{H_s}
. If
H
⊂
G
H \subset G
with
H
2
(
H
,
g
/
h
)
=
0
{H^2}(H,g/h) = 0
, then there is a universal “weak” analytic deformation of H, whose base space is a manifold with tangent plane canonically identified with
Ker
δ
1
\operatorname {Ker} {\delta ^1}
.